Kant\u2019s Antinomies of Pure Reason and the \u2018Hexagon of Predicate Negation\u2019

Peter Mclaughlin,Oliver Schlaudt

doi:10.1007/s11787-020-00240-7

Abstract

Based on an analysis of the category of “infinite judgments” in Kant, we will introduce the logical hexagon of predicate negation. This hexagon allows us to visualize in a single diagram the general structure of both Kant’s solution of the antinomies of pure reason and his argument in favor of Transcendental Idealism.

Highlights

Negation is an essential feature of communication and thought; and natural languages offer various ways for negating assertions and for making negative claims
For which sentential negation can be ambiguous ([7], 364), the unambiguous sentential negation is most closely approximated by sentences like “It is not true/it is not the case/it is false, that S is P”
What is the difference according to Kant between denying (‘removing’) P and asserting (‘positing’) non-P? Kant’s own explication of the difference is not very forthright, given its purported significance for the “dialectical inferences of pure reason,” and it is marred by ambiguities and even typographical errors

Summary

Introduction

Negation is an essential feature of communication and thought; and natural languages offer various ways for negating assertions and for making negative claims. S is non-P”, depending on whether the negation is applied to the whole proposition, the copula, or the predicate All of these statements involving S and P contain a negative particle. For which sentential negation can be ambiguous ([7], 364), the unambiguous sentential negation is most closely approximated by sentences like “It is not true/it is not the case/it is false, that S is P” Such examples contain semantic terms like ‘true’ and ‘false’ which are foreign to the object language of formal logic. Form 3, the use of negative predicates, attracted even less attention Frege dismissed it without further ado on the grounds that the question of how to deal with affixal negation, i.e. negative/negated predicates of the type ‘un-P’, ‘in-P’, or ‘P-less’ like unintelligible, infinite, immortal, fearless, and so on belongs to semantics, not logic [6]. The logical hexagon allows us to visualize in a single diagram the logical structure of the antinomies and of the main dialectical argument of the Critique of Pure Reason in favor of transcendental idealism

Infinite Judgments in Kant’s Logic

The Hexagon of Inner Negation

Inner Negation and Kant’s Solution of the Antinomies of Pure Reason